Question

) Which expressions are equivalent to 35? Choose ALL that apply.

9.27
81.3
3.5
3.3.3.3.3
9.9

Answer 1

`(a)\ 9 * 27`

`(b)\ 81 * 3`

`(d)\ 3*3*3*3*3`

Explanation:

Given

`3^5`

Required

Select equivalent expressions

`(a)\ 9 * 27`

Express as exponents

`9 * 27 = 3^2 * 3^3`

Apply law of indices

`9 * 27 = 3^{2+3`

`9 * 27 = 3^{5`

`(b)\ 81 * 3`

Express as exponents

`81 * 3 = 3^4 * 3`

Apply law of indices

`81 * 3 = 3^{4+1`

`81 * 3 = 3^5`

`(c)\ 3*5`

Solve

`3*5 = 15`

`(d)\ 3*3*3*3*3`

From calculator, we have

`3*3*3*3*3=243`

Express as exponents

`3*3*3*3*3=3^5`

`(e) 9 * 9`

Express as exponents

`9 * 9= 3^2 * 3^2`

Apply law of indices

`9 * 9= 3^{2+2`

`9 * 9= 3^4`

Hence, a, b and d are true